A horizontal rope pulls a 10kg wood sled across frictionless snow. A 5kg wood box rides on top of the sled. What is the largest tension force for which the box doesn't slip. Assume friction coefficient as 0.44
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When the wood sled start to travel due to the pull the small wooden box also start to travel. If we assume that tension force of rope is T then by the Newtons second law of motion ;
T = (5+10)*a where a is the acceleration.
When T increases acceleration will also increase. But initially the wooden box travel with the wood sled due to friction force between wood sled and wood box. When T increases maximum friction force the wooden box will start to slip.
Using F = ma to the whole system
`T_(max) = (5+10)*a`
`a = T_(max)/15 `
Since the small box travel together with the wood sled before it slips it has the same acceleration as the whole system.
Using F = ma to the small box at slip
friction force = m*a
`0.44*5*9.81 = 5*T_(max)/15 `
`T_(max) = 64.746N`
So the maximum tension of the rope is 64.746N
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